Solve for x: 3²x-1 = 27.

Write both sides with the same base: $27=3^3$, so $3^{2x-1}=3^3$. Equal bases mean equal exponents, so $2x-1=3$, then $2x=4$ and $x=2$, choice C. Check: $3^{2(2)-1}=3^3=27$. Choice A ($x=1$) gives $3^1=3$. Choice B ($x=1.5$) comes from setting $2x=3$ and forgetting to add the $1$, giving $3^2=9$. Choice D ($x=4$) stops at $2x=4$ and forgets to divide by 2, giving $3^7$, far too large. Rewriting to a common base is the key move for exponential equations like this one.